Some results related with the generalized and the extended hecke groups

In our thesis, generalized and generalized extended Hecke groups were examined. Our work consists of five parts. In the first part of the thesis, generalized and extended generalized Hecke groups are explained. In the second part of the thesis, the definitions, theorems, concepts and explanations used in the thesis are given. In the third part of the thesis, a theorem containing the conjugate classes of the finite order elements in the generalized and extended Hecke groups was found and the representatives of these conjugate classes were examined with examples. In the fourth part of the thesis, the normal subgroups of generalized Hecke groups with zero genus are examined and examples are given. In the fifth part of the thesis, the results are given and suggestions are made for the studies to be done.